Muchova, who returned to action in June, needed medical treatment on multiple occasions during the second set but held on to dispatch the Brazilian 22nd seed in 85 minutes.
"A little weird match, I have to say," Muchova said in her on-court interview after reaching her fourth career Grand Slam semi-final.
"I had little problems, I wouldn't like to comment on it actually if it's fine. But I'm happy I managed it, to run to the bathroom and back. Sorry if it disturbed anyone, but I had no other choice."
Muchova made a fast start as she grabbed a 4-0 double break lead, held to love and, after Haddad Maia finally got on the board, closed out the opening set on serve.
Haddad Maia improved in the second set but Muchova, who suddenly began grabbing her hip between points, unleashed a backhand winner to break for a 3-2 lead before leaving the court with the physio.
The players exchanged breaks over the next two games before Muchova, after having the physio and doctor at her chair, held to reach 5-3 before taking advantage of new balls and sealing victory on her serve with an ace on her first match point.
"The new balls, it goes faster. You can put more spin so when I heard it was new balls (in the final game) I was actually pretty happy," said world number 52 Muchova after improving to 4-0 in career meetings with Haddad Maia.
"I was trying to put the first serves in. I knew it could make some problems so it was nice in the last game."
Haddad Maia, the first Brazilian woman to make the US Open quarter-finals since Maria Bueno in 1968, also required medical attention late in the match when she appeared to be having difficulty breathing.
Muchova, who has not dropped a set at the year's final Grand Slam, will next face either top seed Iga Swiatek or American sixth seed Jessica Pegula for a place in the final.
